Icahn, now the company's second-largest shareholder after buying 72 million shares from fellow activist investor Southeastern Asset Management Inc., wants the company to buy back up to 1.1 billion Dell shares at $14 apiece to boost shareholders' return on their investment. The price of the buyback would represent about two-thirds of Dell's current market value of about $23.5 billion.

Dell and other personal computer makers have seen their sales crumble because of the growing popularity of smartphones and tablets. In May, Dell posted a 79 percent decline in earnings for the most recent quarter. Michael Dell believes he can turn the company around by taking it private and diversifying into niches, such as business software, data storage and consulting. He and the investment firm Silver Lake Partners are bidding to take the company private for $24.4 billion, or $13.65 per share.

But Icahn and Southeastern say that offer short-changes shareholders and originally proposed that the Round Rock, Texas, company instead give shareholders a special dividend of $12 in cash or stock per share. That would have allowed shareholders to get cash and stay invested in the company.

Dell's board rejected that proposal and has asked shareholders to approve the offer from Michael Dell and Silver Lake in a July 18 vote. In a letter to shareholders on Tuesday, Icahn wrote that he's concluded that Dell's board will never accept his dividend proposal over Michael Dell's offer, and thus is pushing for the buyback to boost shareholder value.

Dell shares rose 7 cents Tuesday to finish at $13.48, a sign that investors aren't taking Icahn very seriously and still expect the buyout deal to go through.

Icahn is now the company's biggest independent shareholder with about 152.5 million shares or an 8.7 percent stake, second only to Michael Dell's 273 million shares, or 15.6 percent stake. Southeastern now holds about 74 million shares, or a 4.2 percent stake.

A special committee of Dell's board said Tuesday that Icahn's latest proposal lacks adequate financing or a commitment from anyone to participate. The proposal "would likely force shareholders to continue to own shares in the highly leveraged company that would result," it added.

Icahn contends that the proposed share buyback would be paid for with $5.2 billion in debt, $7.5 billion in Dell cash and $2.9 billion from the sale of Dell receivables. He said he would make available $2 billion if needed, and said that a major investment bank, which was not named, has agreed to put up $1.6 billion.

Icahn said he and Southeastern would not tender their shares into the $14 per share offer. Other shareholders would be able to sell at least 72 percent of their positions.